A reel of flat blade has an outer diameter of 1016 mm and an inner
diameter of 508 mm. The blade thickness is 20 mm. Could you tell me
the length of the blade and show me the formula for working it out?

I'm trying to construct a pool frame out of pvc that will be placed over
a pool. We already have the pool tarp, but we need to build something
that will shed water so it has to have a slope. PVC only comes in 90
degree and 45 degree angles and straight sections. How do I figure out
the maximum height the frame can stick straight up in the air to utilize
the tarp?

If I measure a cylinder for roundness with a standard OD micrometer I
find a 0.008' difference at 0 degrees and 90 degrees. If I use a 3
point ('V') micrometer I find a 0.001' difference at the same two
positions. Why are they different? Which is better?

Landscaping a fence leads to fractional pickets and frustration. After diagramming a
bird's eye view of a model fence line, Doctor Peterson applies some algebra to the key
insight: in a straight run of fencing, the spaces between the pickets outnumber the
pickets by one.

What is the name of a rectangle with two rounded ends, like a circle
with top and bottom evenly truncated? For example, an 'oval' racetrack
with two straightaways on opposite sides, parallel to each other and
both of the same length. I know that's not really an oval, but I'm
not sure what else to call it!

"What size HD TV do I buy so that its screen is at least as tall as my
old TV's was?" Doctor Rick provides some consumer guidance by calling
on the Pythagorean Theorem and television industry aspect ratios; then
explains how a trigonometric approach arrived at the same conclusion.

To make a funnel, we take a circular piece of metal, cut out a sector,
and connect the two radial edges together to make an open cone. What
should the angle of the sector be to maximize the volume of the cone?

I am trying to calculate the midpoint between cases of legionella and
their nearest neighbor. How can I calculate the distance between two
points below which they can be treated as if they were in a plane
rather than on a sphere?